document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167773>Question 167773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, the following question is from a past exam paper on algebra & complex numbers that I am looking at in order to revise for my Calculus exam.  I have the answer in front of me, but I do not quite understand the working behind it, so if you could clear that up for me I would be grateful.\r<BR>\n" );
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document.write( "QUESTION SIX<BR>\n" );
document.write( "Solve the following equation for x in terms of q:  2^(3x-1)=7^(x-q)\r<BR>\n" );
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document.write( "The assessment schedule says that the answer should be: x=(ln2-qln7)/(3ln2-ln7) or equivalent </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123669 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283x-1%29=7%5E%28x-q%29 ALIGN=MIDDLE  ALT=\"2%5E%283x-1%29=7%5E%28x-q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%5E%283x-1%29%29=ln%287%5E%28x-q%29%29 ALIGN=MIDDLE  ALT=\"ln%282%5E%283x-1%29%29=ln%287%5E%28x-q%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides. This step is needed since the variable we want to solve for is in the exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29ln%282%29=%28x-q%29ln%287%29 ALIGN=MIDDLE  ALT=\"%283x-1%29ln%282%29=%28x-q%29ln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5Ey%29=y%2Aln%28x%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%5Ey%29=y%2Aln%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2Aln%282%29-ln%282%29=x%2Aln%287%29-q%2Aln%287%29 ALIGN=MIDDLE  ALT=\"3x%2Aln%282%29-ln%282%29=x%2Aln%287%29-q%2Aln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2Aln%282%29-x%2Aln%287%29=-q%2Aln%287%29%2Bln%282%29 ALIGN=MIDDLE  ALT=\"3x%2Aln%282%29-x%2Aln%287%29=-q%2Aln%287%29%2Bln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aln%287%29 ALIGN=MIDDLE  ALT=\"x%2Aln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29 ALIGN=MIDDLE  ALT=\"ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2Aln%282%29-x%2Aln%287%29=ln%282%29-q%2Aln%287%29 ALIGN=MIDDLE  ALT=\"3x%2Aln%282%29-x%2Aln%287%29=ln%282%29-q%2Aln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283%2Aln%282%29-ln%287%29%29=ln%282%29-q%2Aln%287%29 ALIGN=MIDDLE  ALT=\"x%283%2Aln%282%29-ln%287%29%29=ln%282%29-q%2Aln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF \"x\" from the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29 ALIGN=MIDDLE  ALT=\"x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aln%282%29-ln%287%29 ALIGN=MIDDLE  ALT=\"3%2Aln%282%29-ln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate \"x\"\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29 ALIGN=MIDDLE  ALT=\"x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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